Self-Organized Evolutionary Process in Sets of Interdependent Variables near the Midpoint of Phase Transition in K-Satisfiability

Abstract

We present a mathematical model of sets of interdependent variables near the midpoint of phase transition in K-Satisfiability, and analyze model.s behavior under perturbation. Surprisingly, when noise is introduced into the perturbation pattern, the model reveals a self-organized evolutionary process driven purely by criticality. The self-organized evolution discovers the interdependencies between the variables, which make some partial solutions more persistent in the presence of noise. The model suggests that a higher sensitivity to perturbation near the midpoint of the phase transition is responsible for a higher sophistication in larger sets of interdependent variables, such as organisms with a larger number of genes, larger ecologies and economies, and larger brains throughout the species.